Download 6.5 Trapezoids and Kites

Trapezoids and Kites
Geometry
Unit 12, Day 5
Mr. Zampetti
Adapted from a PowerPoint created by Mrs. Spitz
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Using properties of trapezoids

A trapezoid is a
quadrilateral with
exactly one pair of
parallel sides.
 The parallel sides
are the bases.
A
base
leg
leg
D
B
base
C
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Using properties of trapezoids

A trapezoid has two
pairs of base angles.
For instance in
trapezoid ABCD D
and C are one pair
of base angles. The
other pair is A and
B.
 The nonparallel sides
are the legs of the
trapezoid.
A
base
leg
leg
D
B
base
C
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Using properties of trapezoids

If the legs of a
trapezoid are
congruent, then the
trapezoid is an
isosceles trapezoid.
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Trapezoid Theorems
Theorem 9-16
 If a trapezoid is
isosceles, then each
pair of base angles
is congruent.
 A ≅ B, C ≅ D
A
D
B
C
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Trapezoid Theorems
Theorem 9-17
 A trapezoid is
isosceles if and only
if its diagonals are
congruent.
 ABCD is isosceles if D
and only if AC ≅ BD.
A
B
C
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Ex: Using properties of Isosceles Trapezoids

PQRS is an
isosceles trapezoid.
Find mP, mQ,
mR.
m RQ = 2.16 cm
m PS = 2.16 cm
S
R
50°

mR = mS = 50°.
P

mP = 180°- 50° =
130°, and mQ =
mP = 130°
Q
You could also add 50 and 50,
get 100 and subtract it from
360°. This would leave you
260/2 or 130°.
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Using properties of kites

A kite is a
quadrilateral that has
two pairs of
consecutive
congruent sides, but
opposite sides are
not congruent.
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Kite theorems
Theorem 9-18
 If a quadrilateral is a
kite, then its
B
diagonals are
perpendicular.
 AC  BD
C
D
A
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Ex. 4: Using the diagonals of a kite



WXYZ is a kite so the
diagonals are
perpendicular. You
can use the
W
Pythagorean Theorem
to find the side
lengths.
WX = WZ = √202 + 122 ≈ 23.32
XY = YZ = √122 + 122 ≈ 16.97
X
12
20
U 12
Y
12
Z
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt
Venn Diagram:
http://teachers2.wcs.edu/high/rhs/staceyh/Geometry/Chapter%206%20Notes.ppt#435,22,6.2 – Properties of Parallelograms
Flow Chart:
http://www.quia.com/pop/103618.html?AP_rand=172732766
Properties of Quadrilaterals

http://www.quia.com/pop/103618.html?A
P_rand=172732766
Homework:

Work Packet: Trapezoids and Kites
http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt